The Rossoneri coach was satisfied with his team's attitude against Juventus, but conceded that they have work to do in defence
The Rossoneri were beaten 3-2 by Juventus in Sunday's Trofeo Berlusconi game, and the 45-year-old was not too impressed with his side's performance at the back.
"I think we definitely conceded goals in the game tonight [Sunday] that could have been avoided if we can work a little better at the back. That is something we will have to do," Allegri stated at a press conference.
"Tonight [Cristian] Zapata was new. Zapata and [Mario] Yepes had never played together before, so we most certainly need to improve.
"However, overall I am happy because the spirit of the team was good, which is what we will need for the season to come."
Milan lock horns with Sampdoria this weekend in their Serie A opener.